I owned a Henry Big Boy Steel side gate, and handled many others including X model, and the case hardened octagon barrel as well.
Action: opening and closing the lever action on Henry / Marlin guns (I also owned a Marlin 1894), can just never be as naturally smooth as the Winchester 1892 without a ton of work. The lever on the Big Boy Steel I got was very stiff. The plunger spring needed a good push on the lever to release. Nothing dramatic I mean, but it was clear to me why Henrys aren’t typical in fast lever applications like cowboy action shooting. I am sure you could fix that by opening and closing the lever a million times, polishing all the internals and also trimming the plunger and hammer springs. But that opens up a whole can of worms that I suspect many would not want to entertain.
My 92 on the other hand you can open the action literally with your pinky finger. No modifications were done to the internals of the action. No polishing or greasing anything. The way the parts go together just creates a smoother lever experience which is what I suspect many use to favor Winchester over Henry. I have found all 1892 manufacturers: Rossi, Chiappa, Browning, Mirokou, to all have smoother actions than Henry. Again this is not a bash on Henry, I do like those guns. It’s just how they’re designed.
Fit and Finish is no question Winchesters will be superior. My big boy steel had a “meh” wood to metal fit, that had a couple spots here and there that were off by a few mm. My 1892 wood to metal fit is very close to perfect. My Marlin was nicer than my Henry in this department as well. I’m talking minor differences here fellas, but they are differences nonetheless.
Shooting wise: either gun is accurate to shoot but the 92 lever experience is more satisfying. Winchester all the way.